x.y=30 and x+y=10.3, I end up with
x=(21.83+60.66i)/(-5.15-5.89i).
i is the square root of (-1).
could you please show me how this equation will = 10.3
I am having problem to figure it out.
thank you.
It is a similar problem of having a rectangle of area 30 units and the semi-perimeter is 10.3.
Using calculus, we find that the minimum real semi-perimeter is 2√30=10.95.
Unless you are working with complex numbers, there is a good chance that there is erroneous data in the question. Did you derive the data (like 10.3) from an experiment, or was it calculated from some other sources?
my Teacher gave this problem
Ask the teacher if he/she expects complex roots, which are approx. 5.15±1.86i.
if my teacher expects complex roots, what will be the final answer if i add x+y = 10.3 = ??
thank you
If
x=5.15+1.86i
y=5.15-1.86i
xy=29.98
x+y=10.3
Note that numerical values are rounded (except 5.15).
Do the multiplication as an exercise.
To solve the equation x + y = 10.3 and find the value of x, we can use the information provided x.y = 30.
First, let's solve x.y = 30 for y by isolating y:
y = 30/x
Now substitute this expression for y in the equation x + y = 10.3:
x + (30/x) = 10.3
Multiplying both sides of the equation by x to eliminate the fraction:
x^2 + 30 = 10.3x
Rearranging the equation to have it in standard quadratic form:
x^2 - 10.3x + 30 = 0
Now, we can solve this quadratic equation. However, based on the expression you provided for x, it seems like we are dealing with complex numbers (involving the imaginary unit i).
The given expression for x is:
x = (21.83 + 60.66i) / (-5.15 - 5.89i)
To check if this expression satisfies the equation x + y = 10.3, we can substitute the expression for x and solve for y:
Substituting x = (21.83 + 60.66i) / (-5.15 - 5.89i):
(21.83 + 60.66i) / (-5.15 - 5.89i) + y = 10.3
Now, let's simplify the expression by multiplying the numerator and denominator by the conjugate of the denominator (-5.15 + 5.89i):
(21.83 + 60.66i) / (-5.15 - 5.89i) * (-5.15 + 5.89i) / (-5.15 + 5.89i) + y = 10.3
Expanding and simplifying:
(-113.2649 + 2.3114i + 289.8494i - 353.1914i^2) / (26.5725 + 34.1123i + 34.1123i - 34.8921i^2) + y = 10.3
Since i^2 = -1:
(-113.2649 + 2.3114i + 289.8494i + 353.1914) / (26.5725 + 34.1123i + 34.1123i + 34.8921) + y = 10.3
Now simplify further:
(239.9265 + 292.1608i) / (61.1621 + 74.0046i) + y = 10.3
Dividing the complex numbers using the formula for dividing complex numbers:
[(239.9265 + 292.1608i) * (61.1621 - 74.0046i)] / [(61.1621 + 74.0046i) * (61.1621 - 74.0046i)] + y = 10.3
Expanding and simplifying:
[-9265.2902 + 5638.6392i] / [4498.1827 + 5476.9363i] + y = 10.3
Finding the common denominator:
[-9265.2902 + 5638.6392i + 4498.1827y + 5476.9363iy] / [4498.1827 + 5476.9363i] = 10.3
Now, let's separate the real and imaginary parts for the left side of the equation and equate them to the real and imaginary parts of 10.3:
Real part:
[-9265.2902 + 4498.1827y] / [4498.1827 + 5476.9363i] = 10.3
Imaginary part:
[5638.6392i + 5476.9363iy] / [4498.1827 + 5476.9363i] = 0
We can solve these two equations simultaneously for real and imaginary values of y. However, it seems like there may be a mistake or confusion in the original equation or the given expression for x. Please double-check your calculations or provide any additional information to help us understand the problem better.